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A-LevelMathematicsTrigonometry9709/22 · May/June 2023 · Q15 Marks

Solve the equation sec² θ + 5 tan² θ = 9 + 17 sec θ for 0° < θ < 360°.

(a)Solve the equation sec² θ + 5 tan² θ = 9 + 17 sec θ for 0° < θ < 360°.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[M1] Attempt to express equation in terms of secθ only
[A1] Obtain 6sec²θ-17secθ-14(=0) or 14 cos²θ +17 cosθ-6=0.
[M1] Attempt solution of 3-term quadratic equation to find one value of θ, from cos θ = ...
[A1] Obtain 73.4 or greater accuracy.
[A1] Obtain 286.6 or greater accuracy; and no others between 0 and 360.

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About this question

Topic: Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, May/June 2023 Paper 2 Variant 2, question 1.

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